Why doesn't Robin appear in the Justice League and Justice League Unlimited animated series?

From IMDb:

When the series was expanded from Justice League to Justice League Unlimited, producers considered adding Batman's sidekicks, Robin, Batgirl, and Nightwing.

However, DC Comics turned them down, because the Robin/Dick Grayson role was being used on Teen Titans.

There was/is something called "(Bat)-Embargo":

a decision to keep certain DC characters exclusive to certain shows across the television and film medium.

Bruce Timm, the man behind Justice League and Justice League Unlimited said about the Bat-Embargo:

... to tell you the truth, as much as I […] love those characters, I don’t really miss [them] all that much. It’s not like we don’t have tons of other interesting characters to play with.

If I were doing an actual Batman show, and not allowed to use those characters, yeah, that’d be pretty galling, but Batman’s only one ingredient in the Justice League’s brew. The Bat-clan aren’t really essential in any way to the current show ...

• although,

  At one point during the later series Justice League Unlimited, an episode featuring Batgirl was discussed. ... The episode was never produced as the rights to the Batgirl character were not held over and were being used by the team on The Batman at the time

However, in the episode Grudge Match they sidestepped the Bat-Embargo:

Dick Grayson has a blink-and-you-miss-it cameo as Nightwing, shown watching from a rooftop as Canary and Huntress drive their way into Blüdhaven.

• Watch the scene on YouTube

At the time Warner Bros., owners of DC Comics and makers of these shows, had a newly-successful Batman film franchise. As a result, they essentially reserved the Batman "universe" (i.e. his settings, friends, and foes) for those films and for Batman-specific TV series. The end result was that both the Justice League series and Smallville couldn't make extensive use of Batman, Gotham, Robin, Nightwing, etc. Other Justice League members didn't have such a limitation, and so the series saw significant use of their rogues galleries.

Blüdhaven appears briefly in the Justice League Unlimited television series episode "Grudge Match" as the backdrop for a meta-human fighting match organized by Roulette in which female Leaguers under mind control (including Fire, Wonder Woman and Black Canary) fight it out. A signboard at the city's entrance says "Welcome to Blüdhaven". In the same scene, the silhouette of Nightwing appears in a cameo. (Source:Wikipedia)

People don't actually notice but dick grayson and barbara gordon ARE in Justice league 1'st season in the season finale. It's a single minute but if you catch it in the right second. It's when flash, lantern, and wonderwomen are in an alternate reality and Batman is a vigilante rebel against Savages army. Among batmans soldiers you see a couple right before they kiss. A long haired man that resembles Dick and a red headed women resembling Barbara. That isn't a coincidence. You also notice a boy that looks like tim drake and a girl that looks like annie the daughter of clayface. Amazing

Let's not forget that joker is not in JLU either. The reason neither he nor Tim appears is because by the second series, the whole Joker Junior plot unfurled, which forced Batman to dismiss Tim. This part is confusing because the flashback scene was made before either JL series so Bats was still in his TNBA costume. But judging by Joker appearing in season 2 of JL as well as season 1, he kidnapped Drake by the end of JL and died before JLU